Cavities identification in linear elasticity: energy-gap versus L2-gap cost functionals

IF 1.1 4区工程技术 Q3 ENGINEERING, MULTIDISCIPLINARY

Inverse Problems in Science and Engineering Pub Date : 2021-10-06 DOI:10.1080/17415977.2021.1974019

N. Benmeghnia

引用次数: 0

Abstract

We study the geometric inverse problem of cavities identification in linear elasticity equation with partially over-determined boundary data. This work proposes a way to compute the topological derivative based on the topological sensitivity analysis concepts, adopting the energy-gap and the -gap as cost functionals. Then, a comparison of both functionals is presented to determine the best choice for numerical studies. Further, several numerical experiences are shown to explore the efficiency of this method.

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线性弹性中的空腔识别:能量缺口与l2缺口成本泛函

研究了具有部分超定边界数据的线性弹性方程中空腔识别的几何反问题。本文提出了一种基于拓扑灵敏度分析概念的拓扑导数的计算方法，采用能隙和间隙作为代价函数。然后，对两个泛函进行比较，以确定数值研究的最佳选择。此外，还展示了一些数值经验来探索该方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems in Science and Engineering 工程技术-工程：综合

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Inverse Problems in Science and Engineering provides an international forum for the discussion of conceptual ideas and methods for the practical solution of applied inverse problems. The Journal aims to address the needs of practising engineers, mathematicians and researchers and to serve as a focal point for the quick communication of ideas. Papers must provide several non-trivial examples of practical applications. Multidisciplinary applied papers are particularly welcome. Topics include: -Shape design: determination of shape, size and location of domains (shape identification or optimization in acoustics, aerodynamics, electromagnets, etc; detection of voids and cracks). -Material properties: determination of physical properties of media. -Boundary values/initial values: identification of the proper boundary conditions and/or initial conditions (tomographic problems involving X-rays, ultrasonics, optics, thermal sources etc; determination of thermal, stress/strain, electromagnetic, fluid flow etc. boundary conditions on inaccessible boundaries; determination of initial chemical composition, etc.). -Forces and sources: determination of the unknown external forces or inputs acting on a domain (structural dynamic modification and reconstruction) and internal concentrated and distributed sources/sinks (sources of heat, noise, electromagnetic radiation, etc.). -Governing equations: inference of analytic forms of partial and/or integral equations governing the variation of measured field quantities.